Information on Result #946156
Linear OOA(2203, 349533, F2, 3, 21) (dual of [(349533, 3), 1048396, 22]-NRT-code), using OOA 3-folding based on linear OA(2203, 1048599, F2, 21) (dual of [1048599, 1048396, 22]-code), using
- 1 times code embedding in larger space [i] based on linear OA(2202, 1048598, F2, 21) (dual of [1048598, 1048396, 22]-code), using
- construction X4 applied to Ce(20) ⊂ Ce(18) [i] based on
- linear OA(2201, 1048576, F2, 21) (dual of [1048576, 1048375, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 220−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(2181, 1048576, F2, 19) (dual of [1048576, 1048395, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 220−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(221, 22, F2, 21) (dual of [22, 1, 22]-code or 22-arc in PG(20,2)), using
- dual of repetition code with length 22 [i]
- linear OA(21, 22, F2, 1) (dual of [22, 21, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(21, s, F2, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- construction X4 applied to Ce(20) ⊂ Ce(18) [i] based on
Mode: Constructive and linear.
Optimality
Show details for fixed k and m, n and k, k and s, k and t, n and m, m and s, m and t, n and s, n and t.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Linear OOA(2206, 349534, F2, 3, 21) (dual of [(349534, 3), 1048396, 22]-NRT-code) | [i] | NRT-Code Embedding in Larger Space | |
| 2 | Linear OOA(2204, 349533, F2, 3, 21) (dual of [(349533, 3), 1048395, 22]-NRT-code) | [i] | OOA Duplication | |
| 3 | Linear OOA(2205, 349533, F2, 3, 21) (dual of [(349533, 3), 1048394, 22]-NRT-code) | [i] | ||